Let $\mathrm{z},\mathrm{\omega }$be complex numbers such that $\overline{\mathrm{z}}+\mathrm{i}\overline{\mathrm{\omega }}=0$and Arg $\left(z\mathrm{\omega }\right)=\mathrm{\pi }$ then Arg(z) =

$$\begin{gathered} \begin{array}{r}Arg\left(z\omega \right)=\pi \end{array}\Rightarrow argz+arg\omega =\pi ......\left(1\right) \\ \overline{z } +i\overline{\omega }=0\Rightarrow z-i\omega =0\Rightarrow z=i\omega \\ \Rightarrow argz=\frac{\pi }{2}+arg\omega \therefore argz-arg\omega =\frac{\pi }{2}.....\left(2\right) \\ adding \left(1\right) and \left(2\right) \\ 2argz=\pi +\frac{\pi }{2}\Rightarrow argz=\frac{3\pi }{4} \end{gathered}$$